Answer
The bowl is 4 times more massive.
Work Step by Step
We know that the center of mass of the bowl is $-\frac{r}{5}$, and we know that since the mouse hits the edge of the bowl, the location of the overall center of mass is $r-\frac{r}{5}$. Since the bowl moves 1/10 of a diameter, we know that it moves 1/5 of a radius. Thus:
$ (r-\frac{r}{5})m_m=\frac{r}{5}m_b \\ 4m_m=m_b$
